But yes, of course, you cannot train a parrot not to scream anymore than you can train a human not to panic in an emergency (911 operators expect this).....it is an instinctive response (in certain situations) that makes use of a natural vocalization. It can also come about because a need is not being met.
Parrot trainers (calling themselves behaviorists) tend to confuse matters because they are not in fact behaviorists but, as I stated, "trainers" (behavior is a legitimate field of study that makes use of the anatomy and neurochemistry of behavior as it takes place in the brain). Training new behaviors (tricks) is one thing but trying to override natural behaviors is another. Unfortunately there is confusion, and the line between the two is often blurred. This is partly due to use of misleading terms such as "behavior modification" by the industry, most often by those who are marketing their "methods." They don't make money if they don't make it seem like they can solve your problems
Any situation that has a bird panicked or afraid, such as being separated from an individual to which it is socially bonded, can elicit the automatic response of an alarm call. As will stimuli that might cause fear. The former involves a "social-attachment" (a part of all social animals) need that is not being met. This is an instinctive need that subsides only when the comfort of a social partner is found. Many people have been misled into believing that they can ignore (extinction burst) this behavior away but what really happens is that the birds anxiety increases and its stress hormone levels rise. I know of at least one study that correlates levels of stress hormone with feather plucking, and many studies show that frustration leads to stereotypical behaviors or stereotypies. These are repetitive non goal oriented motions.
Okay so that was my two cents, in the end - good luck!
